The roots of the quadratic equation x^2 + 7x + 10 = 0 are -2 and -5.
So let us investigate the query more attentively
The quadratic equation x^2 + 7x + 10 = 0 is a standard form of a quadratic equation and can be solved using the quadratic formula. By substituting the values of a, b, and c in the formula, the roots can be found. In this case, the roots are -2 and -5.
“Mathematics, rightly viewed, possesses not only truth but supreme beauty.” – Bertrand Russell
Interesting Facts:
A quadratic equation is a second-degree polynomial equation that has the form ax^2+bx+c=0.
The quadratic formula is the solution of the quadratic equation in terms of the coefficients a, b, and c, which assures that there are always two solutions of the equation.
The roots of a quadratic equation provide valuable information about the curve of the equation, such as the vertex and the direction of the parabola.
Quadratic equations are applicable in different fields of science, such as physics, engineering, and finance, particularly in determining the maximum and minimum values of functions.
Table:
Quadratic Equation
Standard Form
Roots
x^2 + 7x + 10 = 0
ax^2+bx+c=0
-2, -5
In conclusion, the roots of the quadratic equation x^2 + 7x + 10 = 0 are -2 and -5. This has been achieved through substituting the values of a, b, and c in the quadratic formula. Through the quote from Bertrand Russell, it is clear that mathematics, including solving quadratic equations, is both truthful and beautiful. Additionally, the provided facts on quadratic equations demonstrate their widespread applicability in various scientific fields. The table summarizes the quadratic equation’s details, standard form, and roots.
The video teaches how to find the roots of the quadratic equation x^2 + 7x + 10 = 0 via factorization, using the method of splitting the middle term. The process involves multiplying the quadratic equation by 10x^2, and selecting two numbers that result in a product of 10x^2 and a sum of 7x, then adding x to the expression. This results in two factors, (x+2) and (x+5), which when equated to zero, give -2 and -5 as the roots of the quadratic equation.
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Answer:The roots of the equation x2 + 7x + 10 = 0, is -5 and -2.
Therefore, the roots of the quadratic equation are x = 2 and x = 5. We can observe that the roots of the quadratic equation x 2 – 7x + 10 = 0 are x = 2 and x = 5 in each of the methods.
People also ask
What are the roots of the equation 2 7x 10 0?
The answer is: So, 2 and 5 are two roots of the given equation. Q.
How do I find the roots of a quadratic equation?
Answer will be: All you need to do then is do the opposite of b so since b is negative five b is our opposite of b is going to be positive. Five. So x equals.
What are the roots of quadratic equation x2 7x 0 _____ and _____?
Response will be: Hence, roots of quadratic equation x2+7x=0 x 2 + 7 x = 0 are 0 and -7.
What are the roots of the quadratic equation x 2 )+ 7x 12 0?
In reply to that: So, the values come out to be x=−3,x=−4.
How to find the roots of a quadratic equation?
Answer will be: We have to find the roots of the equation. ✦ Try This: Find the roots of the quadratic equation 6x² + x – 2 = 0 using the quadratic formula The roots of the quadratic equation x² + 2√2x – 6 = 0 by using the quadratic formula are √2 and -3√2 x² – 3√5x + 10 = 0, find the roots of the quadratic equations by using the quadratic formula
How do you solve X X using a quadratic formula?
As an answer to this: Use the quadratic formula to find the solutions. Substitute the values a = 1 a = 1, b = −7 b = – 7, and c = 0 c = 0 into the quadratic formula and solve for x x. Simplify. Tap for more steps… The final answer is the combination of both solutions.
What is the sum of the roots of ax2 + bx + c = 0?
Response will be: We know that the roots of an equation ax 2 + bx + c = 0 by quadratic formula are (-b + √ (b 2 – 4ac)) /2a and (-b – √ (b 2 – 4ac) )/2a. Let us represent these by x 1 and x 2 respectively. Therefore, the sum of the roots of the quadratic equation ax2 + bx + c = 0 is -b/a.
How to solve X 2 -7x +12 0 quadratic equation?
Response to this: x ^ 2 -7x +12 = 0 Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. To use the direct factoring method, the equation must be in the form x^2+Bx+C=0. r + s = 7 rs = 12
How do I find the roots of a quadratic equation?
Example x^2-2x+3=4 -OR- 2x-y=9 Click the button to Solve! This quadratic equation root calculator lets you find the roots or zeroes of a quadratic equation. A quadratic is a second degree polynomial of the form: ax2 + bx + c = 0 where a ≠ 0. To solve an equation using the online calculator, simply enter the math problem in the text area provided.
What is the sum of the roots of ax2 + bx + c = 0?
We know that the roots of an equation ax 2 + bx + c = 0 by quadratic formula are (-b + √ (b 2 – 4ac)) /2a and (-b – √ (b 2 – 4ac) )/2a. Let us represent these by x 1 and x 2 respectively. Therefore, the sum of the roots of the quadratic equation ax2 + bx + c = 0 is -b/a.
How do you solve X X using a quadratic formula?
The response is: Use the quadratic formula to find the solutions. Substitute the values a = 1 a = 1, b = −7 b = – 7, and c = 0 c = 0 into the quadratic formula and solve for x x. Simplify. Tap for more steps… The final answer is the combination of both solutions.
How to solve X 2 -7x +12 0 quadratic equation?
The response is: x ^ 2 -7x +12 = 0 Quadratic equations such as this one can be solved by a new direct factoring method that does not require guess work. To use the direct factoring method, the equation must be in the form x^2+Bx+C=0. r + s = 7 rs = 12
